What kind of network do you have? Wired only, wireless only, wired and wireless? What is the network connection device (hub, switch, router/switch)?
What operating system(s) are involved? Windows XP Home or Professional? Original, Service Pack 1 (SP1), SP2, or SP3?
Are there software firewalls enabled on each computer?
How is the printer connected? Wired or wireless? Is it connected directly to a host computer port (serial, parallel, or USB); a network connection device (hub, switch); or a hardware print server device?
What is the printer make and model? Is it an HP printer? Perhaps you should check manufacturer's web site to verify your printer "driver" is up to date for your operating system(s).
If you google on the exact substring "The print spooler was unable to connect to your printer", you'll find this is or was a common problem. Lots of wild theories and solutions are presented. I trust some sources, e.g. HP or annoyances.org, more than others.